Transcript Classifying Triangles PowerPoint

Classifying Triangles
Unit 4C-Triangle Geometry
LT1: I can classify triangles based on
angle measures.
 LT2: I can classify triangles based on side
measures.

Two Ways to Classify Triangles
By Their Sides
 By Their Angles

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Classifying Triangles
By Their Sides
Scalene
 Isosceles
 Equilateral

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Scalene Triangles

No sides are the same length
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Isosceles Triangles

At least two sides are the same length
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Equilateral Triangles

All three sides are the same length
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Classifying Triangles
By Their Angles
Acute
 Right
 Obtuse

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Acute Triangles

Acute triangles have three acute angles
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Right Triangles

Right triangles have one right angle
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Obtuse Triangles

Obtuse triangles have one obtuse angle
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Classify this triangle.
Right Scalene
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Classify this triangle.
Obtuse Isosceles
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Classify this triangle.
Acute Scalene
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Classify this triangle.
Acute Isosceles
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Classify this triangle.
Obtuse Scalene
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Classify this triangle.
Right Isosceles
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It’s YOUR Turn!
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Now it’s your turn to practice classifying triangles.
Complete Side 1 (LT1-2) of the worksheet
On the bottom half (tic marks on the triangles) classify
the triangles based on BOTH sides and angles. For
example, an acute isosceles
On the top half (no tic marks on the triangles) classify the
triangles based only on angles. For example, acute.
You will have 10 minutes to complete this worksheet
before we discuss your findings as a class.
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Answer Time
1. Acute
10. Acute Isosceles
2. Right
11. Right Scalene
3. Obtuse
12. Obtuse Isosceles
4.
5.
6.
7.
8.
9.
13. Acute Equilateral
14. Obtuse Scalene
15. Right Scalene
16. Acute Isosceles
17. Obtuse Scalene
18. Acute Equilateral
Acute
Obtuse
Acute
Right
Obtuse
Acute
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Any Questions????
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Identifying Triangles
Unit 4C-Triangle Geometry
LT3: I can identify whether given angle
measures form a triangle.
 LT4: I can identify whether given side
lengths form a triangle.

Triangles Based On Angles
 The
sum of all angles in a triangle
MUST equal 180˚!!!!!!!!!!!!!!!
 What does “sum” mean?
 How many angles does a triangle
have?
 If the sum of all angles in a triangle
does NOT equal 180° a triangle
cannot be formed!!!
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Angle Measures
60° + 60° + 60° = 180°
40° + 30° + 110° = 180°
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Examples

Will the following angle measures form a
triangle?
1.)
80°, 40°, 60°
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YES!!!!!!!!!!!!
80°
+ 40° + 60° = 180°
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Examples
2.)
26°, 95°, 60°
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NO!!!!!!!!!!!!
26°
+ 95° + 60° = 181°
Remember, the sum of
all three angles MUST
equal 180°!
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Side Lengths
The Triangle Inequality Theorem states
that any side of a triangle is always shorter
than the sum of the other two sides.
 A + B > C and A + C > B and B + C > A
with A, B, and C being the three sides of
the triangle.
 If ANY of the above is NOT TRUE then a
triangle cannot be formed!

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Triangle Inequality Theorem
Examples

Will the following side lengths form a
triangle?
1.)
10 in, 12 in, 14 in
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YES!!!!!!!!!!!!
10
+ 12 > 14
10 + 14 > 12
12 + 14 > 10
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Examples
2.)
2 cm, 8 cm, 16 cm
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NO!!!!!!!!!!!!!!!!!!
2
+ 8 < 16
 2 + 16 > 8
 8 + 16 > 2

Remember, ALL statements MUST BE
TRUE for a triangle to be made!
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It’s YOUR Turn!


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Now it’s your turn to practice identifying triangles.
Complete Side 2 of the worksheet
On the top half (side measurements) determine if a triangle can
be made or not by placing “Yes” or “No” in the first column.
Then, in the second column, prove or disprove your answer
using the Triangle Inequality Theorem.
On the bottom half (angle measures) determine if a triangle
can be made or not by placing “Yes” or “No” in the first
column. Then, in the second column, prove or disprove your
answer.
You will have 20 minutes to complete this worksheet before
we discuss your findings as a class.
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Answer Time
1. Yes
7. Yes
2. No
8. Yes
3. No
9. No
4. Yes
5. Yes
6. Yes
10. No
11. Yes
12. Yes
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Any Questions????
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